\[x\]	
\[h(x)\]
\[-5\]	
\[6\]
\[-4\]	
\[4\]
\[-3\]	
\[2\]
\[-2\]	
\[0\]
\[-1\]	
\[-1\]
\[0\]	
\[-2\]
\[1\]	
\[-3\]
\[2\]	
\[0\]
\[3\]	
\[3\]
\[4\]	
\[6\]
\[5\]	
\[9\]
Qual a taxa de variação média de 
\[h\] sobre o intervalo 
\[[1,2]\]?
Give an exact number.


A taxa de variação média de uma função \( h(x) \) sobre um intervalo \([a, b]\) é calculada pela fórmula:

\[
\text{Taxa de variação média} = \frac{h(b) - h(a)}{b - a}
\]

Neste caso, o intervalo é \([1, 2]\), então \(a = 1\) e \(b = 2\).

Vamos utilizar os valores dados para \(h(1)\) e \(h(2)\):

\[
h(1) = -3 \quad \text{e} \quad h(2) = 0
\]

Agora, substituímos na fórmula:

\[
\text{Taxa de variação média} = \frac{h(2) - h(1)}{2 - 1} = \frac{0 - (-3)}{1} = \frac{3}{1} = 3
\]

Portanto, a taxa de variação média de \(h\) sobre o intervalo \([1, 2]\) é \(3\).

Would you like more details or have any questions? Here are some related questions to explore:

1. How do you interpret the sign of the average rate of change?
2. What does an average rate of change of zero imply about the function?
3. How can you find the instantaneous rate of change at a specific point?
4. What happens to the average rate of change if the interval is narrowed to a single point?
5. Can the average rate of change be used to determine if a function is increasing or decreasing?
6. How does the average rate of change relate to the slope of a secant line?
7. How can you calculate the average rate of change for a piecewise function?
8. How does the average rate of change differ from the derivative?

**Tip:** The average rate of change of a function over an interval is conceptually similar to the slope of the line connecting two points on the graph of the function.

Learn how to calculate the average rate of change of the function h(x) over the interval [1, 2] with step-by-step explanation. Understand the concept of average rate of change in relation to functions and intervals. Suitable for high school students.

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